Explanation of the Rank-Size Rule Model for AP Human Geography

📚 Understanding the Rank-Size Rule

The Rank-Size Rule is a concept in geography that describes the statistical relationship between the population size and rank of a city within a country. It suggests that the $n^{th}$ largest city in a country or region will be $\frac{1}{n}$ the size of the largest city.

📝 Key Components Explained

• 🥇 Largest City: The biggest city sets the standard. Other cities' sizes are relative to it.
• 🔢 Mathematical Relationship: If the largest city has a population of 1 million, the second largest should have around 500,000 (1/2), the third largest around 333,333 (1/3), and so on.
• 🌍 Application: It provides a way to understand urban hierarchies and population distribution.

🌍 Real-World Examples

• 🇺🇸 United States: While not a perfect fit, the US urban system somewhat aligns with the rank-size rule. New York City is the largest, followed by Los Angeles, Chicago, etc., generally decreasing in size according to the rule.
• 🇩🇪 Germany: Germany exhibits a polycentric urban system, which deviates significantly from the rank-size rule. Berlin is the largest, but there are several other large cities like Hamburg, Munich, and Cologne that prevent a steep population decline based on rank.
• ⚠️ Deviations: Many countries do not perfectly follow the rank-size rule, often due to historical, economic, or political factors.

📈 How to Calculate and Interpret

The general formula is:

$\text{Population of city}_n = \frac{\text{Population of Largest City}}{n}$

• ✍️ Calculation: Plug in the population of the largest city and the rank ($n$) of the city you want to estimate.
• 📊 Interpretation: If the actual population deviates significantly from the calculated population, it suggests unique factors are influencing the city's growth.

💡 Advantages and Disadvantages

• ✅ Advantage: Provides a simple benchmark for understanding urban hierarchies.
• ❌ Disadvantage: Often doesn't perfectly reflect real-world conditions due to various influencing factors.

🤔 Factors Affecting the Rank-Size Rule

• 🏛️ Government Policies: Policies that favor certain cities can disrupt the rank-size distribution.
• 💰 Economic Development: Uneven economic growth can lead to some cities growing much faster than others.
• 🗺️ Historical Factors: Colonial legacies or historical events can shape urban hierarchies.

🧪 Practice Quiz

1. If the largest city in a country has a population of 8 million, what would the Rank-Size Rule predict the population of the 4th largest city to be?
2. Name a country that closely follows the Rank-Size Rule.
3. Name a country that deviates from the Rank-Size Rule and explain why.